Problem: What is Tartarus mentioned here?
Solution: The Greek word for hell here is tartaroō, which is a unique usage in the NT. Blum records, “Tartarus, thought of by the Greeks as a subterranean place lower than Hades where divine punishment was meted out, was so regarded in Jewish apocalyptic as well.” This was the place that gods would be judged, which is referred to in Greek mythology. Of course, Peter isn’t using this term to affirm Pagan mythology. Instead, he is contextually using their term to make his point. This was an appropriate term to describe a place where angels will be judged in hell.
 BAG, p. 813. Cited in Blum, E. A. (1981). 2 Peter. In F. E. Gaebelein (Ed.), The Expositor’s Bible Commentary, Volume 12: Hebrews through Revelation (F. E. Gaebelein, Ed.) (278). Grand Rapids, MI: Zondervan Publishing House.
 Lucas, R. C., & Green, C. (1995). The message of 2 Peter & Jude: The promise of His coming. The Bible Speaks Today (96). Leicester, England; Downers Grove, IL: InterVarsity Press.
“For if God spared not the angels that sinned, but cast them down to hell, and delivered them into chains of darkness, to be reserved unto judgment; (2 Pet 2:4)”